A hearing in Parliament on Tuesday was told AMR is the "biggest single health threat" facing mankind.
It is estimated to cause about 700,000 deaths each year worldwide and around 50,000 fatalities in the EU alone.
The hearing, organised by both the EPP and S&D groups, heard there had been a huge decline in human fatalities from infectious diseases over the years and this was largely due to the advance of vaccinations and antibiotics.
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But AMR - where bacteria and other micro-organisms become resistant to the treatments used against the infections they cause - has become a pressing public health issue.
The term AMR covers resistance to drugs capable of treating infections. The percentage of bacteria that are resistant is increasing and these may eventually become superbugs, such as MRSA which has resulted in dozens of deaths in the UK alone.
Andrea Ammon, the newly-appointed director of the European Centre for Disease Prevention and Control (ECDC), said one of the reasons for the rapid rise in AMR in recent years has been the over-use and misuse of antibiotics.
The lack of development of new antibiotics and gaps in knowledge on AMR also play a role.
Without effective antibiotics, standard medical procedures such as surgery and cancer chemotherapy will become high risk, it was said.
Ammon told the meeting that failure to contain and control the spread of AMR would signal "the end of modern medicine as we know it."
She said that while the situation was very worrying, there was still a chance for the upwards trend to be reversed.
She said, "It is not too late to do something and the tide can be turned but this is going to need leadership, commitment and cooperation."
Active surveillance, whereby all patients are screened on admission for treatment, is one measure that she said could be taken.
Other recommendations included offering medical staff specialised training in infection control and raising awareness of hygiene precautions.
Ammon also said that the prudent use of antibiotics would play a key role in tackling AMR, adding, "This means taking antibiotics only when it is absolutely necessary and in the correct dosage."
Further comment came from EPP group deputy José Inácio Faria, a member of the public health and environment committee, who described AMR as the "biggest global health threat".
The hearing comes ahead of an announcement later this week by the Commission on new measures designed to combat AMR.
Faria said, "This action plan will promote best practice, boost research into AMR and seeks to help shape the agenda. But, clearly, much more still needs to be done."
S&D group member Nicola Caputo called on all member states to come forward with AMR action plans, which he said could help promote further innovation in the area.
He said, "The figures are startling: it is estimated that by 2050 AMR will be responsible for more fatalities in Europe than cancer. The threat is huge and the potential to get even more serious is even bigger. It will mean that even minor infections can lead to serious ill health and even death."
He added, "This is a growing threat but there is no single solution, so collaboration between the different parties is going to be essential."